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BULLETIN OF THE UNIVERSITY OF WISCONSIN 

No. 368: High School Series, No. 9 



SCHOOL AND UNIVERSITY GRADES 



BY 

WALTER FENNO DEARBORN 

Sometime Assistant Professor of Education 

The University of Wisconsin 

Professor of Education 

The University of Chicago 



MADI SON 

Published by the University 

June, 1910 



KotiogwwS 



HIGH SCHOOIi SERIES 



1. Thk High School Coukse in English, by V/illard G. 
Bleyer, Pli. D., Assistant Professor of Journalism. 1906. 1907. 
1009. 

2. The High School Coukse in Gsu^rAN, by M. Blakemore 
Evans, Ph. D., Assistant Professor of German, 1907. 1909. 

3. Composition in the High School: The First and Sec- 
ond Yeabs, by Margaret Aslunun, Insiructcr in Englisli. 190S 
1910. 

4. The High School Course in Latin, by M. S. Slaugliter, 
Ph. D., Professor of Latin. 1908. 

5. The High School Couese in Voice Training, by Rollo 
L. Lyman, Assistant Professor of Rhetoric and Oratory. 1909. 

6. The Relative Standing of Pupils in the High School 
AND IN THE UNIVERSITY, by W. F. Dearbom, Ph. D., Assistant 
Professor of Education. 1909. 

7. A CouKSE IN Moral Instruction for the High School. 
by Frank Chai3man Sharp, Ph. D., Professor of Philosopliy. 
1909. 

8. The High School Course in Mathematics, by E. B. 
Skinner, Ph. D., Assistant Professor of Mathematics. 1909. 

9. School and University Grades, by W. F. Dearborn, Ph. 
D., Assistant Professor of EdiK'atinn. 1910. 



Copies of these bulletins may be obtained by writing the 
Secretary of the Committee on Accredited SchoolS; Room liO, 
University Hall. 



Entered as second-class matter June 10, 1S98, at the post office at 
Madison, Wisconsin, under the Act of July 16, 1H94. 



SCHOOL AND UNIVERSITY GRADES 



BY 

WALTER FENNO DEARBORN 

Sometime Assistant Professor of Education 

The University of Wisconsin 

Professor of Education 
The University of Chicago 



MADI SON 

Published by the University 

June, 1910 



\ V 



3Qfl|fl||^S 
;iva, RECORD 



AflV OF U.. 

AUG 1 1932 



J^' 



CONTENTS. 



I. Introduction 5 

II. The Distribution of Mental Ability 7 

III. Inequalities in Grading 22 

IV. Grades in Different School Subjects 36 

V. The University Grades 43 

VI. The Correlation of Schools and School Subjects 49 

VII. Appendix of University Grades 54 



List of Illustrations. 



Figure 


I. 


Figure 


II. 


Figure 


III. 


Figure 


IV. 


Figure 


V. 


Figure 


VI. 


Figure 


VII. 


Figure 


VIII. 



Figure 



Figure 



IX. 



X. 



Figure 
Figure 


XI. 
XI. 


-A 
-B 


Figure 


XII. 




Figure 


XIII. 


-A 


Figure 


XIII. 


-B 


Figure 


XIV. 


-A 



Stature of 1.025 English women (meas- 
urement by Karl Pearson 9 

EfBciency of 12-year-old pupils in accur- 
acy and rapidity of perception 11 

Memory for related words of Third 
Grade girls 11 

General averages of High School rec- 
ords of 472 pupils 12 

Grades of same 472 pupils in Freshman 
year, University of Wisconsin 13 

Grades of 180 students in the Freshman 
and Senior years. University of Wis- 
consin 13 

Distribution of grades assigned to 2,334 
students 14 

Distribution of grades according to five 
equal divisions — ^the base line of the 
theoretical curve 18 

Distribution of the numerical standings 
of pupils in Grades III-VIII, inclu- 
sive ( City A) 25 

Distribution of the numerical standings 
of pupils in Grades IV-VIII, inclu- 
sive (City B) 27 

High School grades of pupils in English 28 

High School grades of same pupils* in 
Mathematics 28 

Grading of class in Freshman Mathe- 
matics 29 

Ranks of Engineering students in Fresh- 
man English 30 

Ranks of students in College of Letters 
and Science in Freshman English. . . 30 

Ranks of Engineering students in Fresh- 
man Mathematics 30 



Figure XIV.-B Ranks of students in College of Letters 
and Science in Freshman Mathemat- 
ics 30 

Figure XV. Senior class in English (175 pupils)... 33 

Figure XVI. Grades of 244 High School pupils in 

English 38 

Figure XVII. Grades of 146 students in Freshman 

Mathematics 39 

Figure XVIII. Grades of 79 High School students in 

Sophomore English and Mathematics 40 

Figure XVIX. Grades of University Freshmen in His- 
tory and German 40 

Figure XX. Grades of University Freshmen in His- 
tory and Mathematics 41 

Figure XXI. Distribution of the average grades of 
students in first two years at the 
University 42 

Figure XXII. Distribution of the average grades of 
students in last two years at the 
University 43 

Figure XXIII. Distribution of the average grades of 
students for the four years at the 
University 45 

Figure XXIV. Redistribution of grades shown in Chart 

23 46 

Figure XXV. Comparison of the distribution of the 
average grades of a group of stu- 
dents in High School and University 52 

Figure XXVI. Comparison of grades of students in 

High School and Freshman English. 52 

Figure XXVII. Comparison of grades of students in 

High School and Freshman German. 53 

Figure XXVIII. Comparison of grades of students in 
High ochool and Freshman Mathe- 
matics 53 



Plate I-A. High School Grades in Latin Facing page 49 

Plate I-B. High School Grades in English... " " 49 

Plate I-C. High School Grades in Mathematics " " 49 

Plate I-D. Freshman Year University " " 49 

Plate 1-E. Freshman Year High School " " 49 



Table I-A. Percentages by Departments — Freshman and 

Sophomore Years 54 

Table I-B. Percentages by Departments — Junior and Sen- 
ior Years 55 

Table I-C. Percentages by Departments — All classes 55 

Table II-A. Percentages of grades assigned to individual 

instructors to Freshmen and Sophomores.. 56 

Table II-B. Percentages of grades assigned by individual 

instructors to Juniors and Seniors 57 



I. INTRODUCTION* 

School grades ai'e usually regarded somewhat differently 
by teachers and pupils. Their assignments frequently entail 
upon the teacher a painstaking routine, the results of which, 
although generally performed conscientiously, are often un- 
satisfactory. The grades may appear to the teacher to stand 
for real differences in ability between pupils or the merely 
temporary successes or failures in a series of tests and quizzes; 
often he is not certain after all his pains that they represent 
the facts accurately in either case. In the hands of some 
teachers, marks appear to be used as incentives or as rewards 
and punishments. Some are generous in their assignment, 
others niggardly in the use of good grades. Because of these 
and many other differences easily suggested in the use and sig- 
nificance of marks, teachers generally minimize their impor- 
tance. It is rather exceptional, on the other hand, to find stu- 
dents who are not more or less concerned about the teacher's 
estimate of their abilities or attainments. Although the stu- 
dent is properly urged and warned not to work for marl^, 
they are, after all, about the only concrete evidence he has in 
many cases of his success or failure. Some students notorious- 
ly elect courses because they secure high grades in them and 
shun others because they cannot do so. Some find their inter- 
ests more or less determined by courses in which they appar- 
ently succeed, — for nothing fixes interest quite as much as suc- 
cess. And a high mark is often considered evidence of success 
and a low mark of incapacity or failure, which, of course, in 
any given case it may or may not be. Some students, I have 
no doubt, determine their election of studies, if not their per- 
manent scholastic interest indirectly at least by the fact that 
they have attained this sort of success in introductory or ele- 
mentary courses of study. And the grades may have been 
meaningless. One instructor was generous, another severe, or 
what not in his estimate of the pupil's work. These are ques- 
tions which certainly deserve some consideration, but when we 



*The writer is indebted to Dean E. A. Birge, Professor E. B. 
Skinner of the University of Wisconsin, and to Professor E. L. 
Thorndlke of Columbia University for suggestions and criticisms 
by which he has benefited during the progress of this study. 



6 THE UNIVERSITY OF WISCONSIN 

assume to exclude pupils altogether from school or college or 
from certain lines of work on the basis of grades and examina- 
tions, the latter take on an even greater importance. Professor 
J. McKeen Cattell, several years ago commented as follows on 
this aspect of school marks: 

"In examinations and grades which attempt to determine 
individual differences and to select individuals for special pur- 
poses, it seems strange that no scientific study of any conse- 
quence has been made to determine the validity of our meth- 
ods, to standarize and improve them. It is quite possible that 
the assigning of grades to school children and college students 
as a kind of reward or punishment is useless or worse; its 
value could and should be determined. But when students are 
excluded from college because they do not secure a certain 
grade in a written examination, or when candidates for posi- 
tions in government service are selected as a result of a 
written examination, we assume a serious responsibility. The 
least that we can do is to make a scientific study of our meth- 
ods and results." "' 

Many cases of inequality, and occasionally of injustice, may 
undoubtedly be discovered in the grading of pupils from the 
elementary schools to the university. When, however, teach- 
ers are allowed to follow their own methods, and not asked 
to discriminate too minutely between different grades of abil- 
ity, it is unusual to find important differences of opinion among 
even very large numbers of instructors. The following study 
will bear out the statement that such inequalities as exist are 
not so much due to unfairness on the part of teachers, or to 
real differences in the estimation which different teachers place 
on the same pupil's work or abilities, as to the fact that the 
standards of measurement employed are not uniform, or are 
used differently by different men. 

The facts presented in regard to the prevailing conditions 
in the grading of pupils are based on a study of fifteen thou^ 
sand or more grades, assigned by about two hundred and fifty 
teachers in several elementary and high schools, and in the 
College of Letters and Science of the University of Wisconsin. 
Since, as just stated, the chief causes of inequality are, it is be- 
lieved, due to lack of uniformity in standards, certain pro- 



<^> Popular Science Monihli/, 66. 



SCHOOL AND UNIVERSITY GRADES 7 

posals making toward such uniformity of practice will first be 
reviewed. In tiie last chapter various ways of using school 
marks in the investigation of several important school prob- 
lems are suggested. The object is to indicate ways by which 
the vast amount of labor expended by teachers in the grading 
of their students, may be made to serve some further purposes 
in the study of problems which concern the efficiency of school 
work. 

The discussion which follows in regard to the intelligent 
use of school marks leaves, the author is well aware, many 
points open to criticism. Some of this might be met if the 
scope of the article admitted of a fuller discussion. If the pro- 
posals appear to teachers theoretical and mechanical in their 
operation, considerable justification may be found for them in 
the fact that an examination of the systems of marking in 
vogue in almost any of our schools and colleges show lack of 
uniformity and striking inequalities. The proposals supply 
certain standards which will make for uniformity and equality 
where these are too frequently wanting. 

II. THE DISTRIBUTION OF MENTAL ABIIilTY 

Galton, Pearson, and others have held that individuals dif- 
fer from each other in ability in such ways that these differ- 
ences conform to the general biological law of variation; in 
9ther words, that ability and attainment are distributed in ac- 
cordance with the curve of error. In discussing the early work 
of Galton in this field. Professor Brooks has made the follow- 
ing clear statement of the case in regard to physical char- 
acteristics: 

"If we select any one characteristic of a group of animals, — 
such a characteristic as the weight of the individuals, or the 
ratio between the length of their arms and legs, or anything 
else which admits of exact numerical statement, — it will be 
found that, while no two members of the group are exactly 
alike, they nevertheless conform to a type, and show the exist- 
ence of a standard, the mean or average, to which the majority 
adhere pretty closely, while other members of the group may 
be more abnormal, showing marked deviation from the mean. 
The deviation of these abnormal individuals from the mean 
is not accidental or due to chance, for it is part of the orderly 



8 THE UNIVERSITY OF WISCONSIN 

system of nature. If the cases tabulated are numerous enough, 
the individuals will conform, so far as this quality is concern- 
ed, to what is known in statistical science as the law of fre- 
quency of error. This agreement will be so close, when great 
numbers of individuals are compared, that the number which 
depart from the mean to any specified degree may be computed 
mathematically. 

For example, the chest measurement of 5,738 soldiers gave 
the following results: — 



Inches 


Measured 


Computed 


33 


5 


7 


34 


31 


29 


35 


141 


110 


36 


322 


323 


37 


732 


732 


38 


1305 


1333 


39 


1867 


1838 


40 


1882 


1987 


41 


1628 


1675 


42 


1148 


1096 


43 


645 


560 


44 


160 


221 


45 


87 


69 


46 


38 


16 


47 


7 


3 


48 


2 


1 



If the number of events had been five hundred thousand or 
five million, instead of five thousand, the agreement between 
the computed and observed frequency of each degree of de- 
parture from the mean would have been very much closer. 
When the number of cases is unlimited, the agreement is per- 
fect." "' 

The form of the theoretical curve, — the probability in- 
tegral, — corresponding to the column of results in the above 
table, and according to which these physical characteristics 
appear to be distributed is given in Figure 1. The dotted line 
represents the normal curve, the heavy line the approximate 



(1) Brooks, The Foundation of Zoolog,!/, pp. 156-157. 



SCHOOL AND UNIVERSITY GRADES 




i>7 i^ 6J ID 

stature of 1,025 English Women. (Measured by Karl Pearson.) 

distribution in stature of 1,025 English women measured by 
Karl Pearson. '-' 

There is considerable evidence that what is true of phys 
ical characteristics holds also for mental. In the matter of 
general intelligence, we speak of idiots, feeble minded, defi- 
cient, backward, dull, those of ordinary or average ability, the 
bright, the brilliant, the man of talent or genius, and of many 
finer distinctions. The majority of people stand between the 
extremes in the medium classes, — are "about average;" those 
who are either deficient or gifted are the exceptional, th-; 
greater the extent of their deficiency or their endowment, th*^ 
fewer there are in either case. 

"And in general the form of distribution is such that be- 
tween very many individuals the differences are little, that 
between many they are moderate, and that between only a few 
are they great. In any group of the same general class with 
respect to age or training, such a clustering of the cases, com- 



<2) Quoted by Q.zXi.&\\, Poi>ular Science Monthly , 66: 371. 



10 THE UNIVERSITY OF WISCONSIN 

monly around a medium degree of the ability, will be the case. 
Individuals, that is, vary about a central type, so that we can 
think of any single individual's ability as a plus or a minus 
deviation from the central tendency of his age, sex, or 
grade." <"' 

In the more specific mental traits, as, for example, in per- 
ception and memory, we find similar differences. The two 
curves plotted below will serve as examples. The heavy lines 
denote the frequency of cases, the dotted the theoretical curve. 
The first gives the result of a test of efficiency of twelve year 
old pupils in the rapidity and accuracy of perception of a spe- 
cial sort. (Figures 2 and 3), (Figures 7 and 15, from Thorn- 
dike, Educational Psychology, p. 15). The second shows the 
memory of related words in the case of third grade girls. 
(Figure 3.) "' 

The bearing of all these facts on the question of school 
marks is not far to seek. Marks, representing as they do the 
teacher's estimate of mental abilities of various sorts, may 
themselves naturally be distributed according to the same 
frequencies as are the abilities which they are designed to 
represent. In so far as the teacher's judgment is correct and 
is made of a sufficiently large number of pupils, the frequency 
of the different marks given should be the same as in a "nor- 
mal" distribution curve. If the teacher has to do only with 
small classes, the results of several years' marking or of sev- 
eral classes in the same subject in the same year should, when 
put together, be similar to the marks of a larger group given 
at one time. 

This general thesis will be subjected to some modification, 
and will need further justification and explanation in the fol- 
lowing discussion. One objection to it may possibly be men- 
tioned at the start. 

Marks, it may be said, are usually given as indications of 
attainment and not necessarily of ability. An extremely bright 
boy may be lazy and accomplish little by his abilities and a 
dullard may by application accomplish relatively more than 
his abilities warrant. While this is undoubtedly a pertinent 



<•" Thorndike, Principals of Teaching, pp. 70-71. 

<^' For other examples and a concise and illuminating- discussion 
of this subject see the chapters in Thorndike's Principles of Teaching, 
and Educational Psychology, referred to. 



SCHOOL AND UXIVERSITY GRADES 




Efficiency of l:2-year-old pupils in accuracy and rapidity of 
perception. (Tliorndike, Ed. Psych.) 



!HimUm;il!!!Jl!milH:l-HHiHtfh~4 



gt?: g|rftti^ip;!!Uiji:!i!iyijmUif^ 




Jfi^ 6* 



Memory for related words of Third grade girls. 



12 



THE UNIVERSITY OF WISCONSIN 



objection, such instances are the exception rather than the 
rule; and in the long run, those who excel do so because they 
are naturally superior, and those who fail, fail mainly on ac- 
count of inferior ability. 

The strongest argument, however, for such a distribution 
of marks as that proposed, is that it is the one usually found, 
especially when a fairly large number of students are graded. 
In Figure 4, the heavy line represents the general averages of 




General Averages of High School Records of 472 pupils. 

the high school records of 472 pupils who entered the College 
of Letters and Science of the University of Wisconsin from the 
larger high schools of the state. The dotted line shows the 
corresponding frequencies of the probability integral. Figure 
5 gives the distribution of the grades of the same pupils in the 
freshman year in the university. The distribution in Figure 
5 fits very closely indeed into the theoretical curve. In the 
freshman year, the chief difference is in the assignment of 
relatively too many ranl^s of "good" and too few of "fairs" and 
"poors" to agree with the theoretical curve. 

Figure 6 shows a similarly close approximation in the case 
of both curves. The heavy line represents the standings of 



SCHOOL AND UNIVERSITY GRADES 



13 




s 80!^ 



Grades of same 472 pupils (Cp. Fig. 4) in Freshman year, 
University of Wisconsin. 







7^17^73>.75J76J57>^^^ Sd$i8Z81 Sites 8h 8) 88 %9^o^nn JM^ft, ?)n 

Grade of 180 students in University of Wisconsin. 



14 



THE UNIVERSITY OF WISCONSIN 



180 students in the freshman year at the university; the dotted 
line the standings of the same students in the senior year. 

It is evident from the dotted line representing the general 
averages of ISO students in the senior year that the distribu- 
tion is about normal, although the average or median of the 
class has been raised to 87 (median), whereas for these same 
students in the freshman year it was 85. This comparison in- 
cludes only those pupils who remain through the four years 
at the university. The very poorest students are therefore not 
taken into account, but considering the same 180 pupils in 
their freshman and senior years, it appears that this grading 
is not remarkably different, and is in each case according to a 
normal distribution. 

A fairly close approximation is also found in a curve pub- 
lished by Professor W. S. Hall, giving the distribution of the 
marks assigned by him to 2,334 medical students in the course 
of ten years. The dotted line in Figure 7 represents the bi- 
nomial curve. 




SOtbO 70 7S SO i<> ^0 % JDO 



SCHOOL AND UNIVERSITY GRADES 15 

Professor Hall makes the following statements in explana- 
tion of his curve: 

"That the curve derived from the rating of 2,334 students 
is really a binomial curve no fair-minded judge would for a 
moment question or doubt. We have, therefore, demonstrated 
beyond cavil that examination data is biologic data and obeys 
the laws of distribution of biologic data. 

"Certain important divergences from strict coincidence re- 
main yet to be explained. Why does the apex of the curve 
stand to the right of the symmetrical binomial curve; i. e., 
why is the curve of my ratings unsymmetrical? The answer is 
to be sought in two directions: 

"1. Either the examiner was too generous and habitually 
rated his students above their equitable deserts; or 

"2. The students were (in a sufficient number of indi- 
vidual cases to influence the totals) guilty of raising their 
rating above what it should be by nature through dishonest 
mea,ns or extraneous aids in quizzes, examinations and the 
preparation of note books. 

"I am convinced that both of these factors were at work, 
and in the same direction, i. e., both tended to raise the rating 
of students and thus to throw the curve out of symmetry. To- 
gether these two factors have made a difference of approxi- 
mately five per cent — the actual median value of the rating of 
the 2334 men being 85.15 per cent when theoretically it should 
have been 80 per cent." 

The reasons why the distribution of Professor Hall does 
not follow more closely the normal distribution need not in- 
clude suggested unfairness or cribbing, on the part of students. 
On this basis it would be hard to account for those who do 
poorer than the normal distribution would call for. A con- 
siderable number of the latter cases exist, although not as 
many as of those who secure higher ranks in excess of the nor- 
mal requirement. The more acceptable explanation is, simply 
that the instructor in question gave more high grades and 
somewhat more low ones than were to have been expected in 
a normal distribution. The factor of selection may of course 
also enter as an explanation of the larger number of high 
marks; that is, college students are a somewhat selected group 
and thus should possibly be graded somewhat higher than a 



16 THE LIXIVERSITY OF WISCONSIN 

group of people selected at random would be. It is hardly 
possible, however, as noted below, to take account of this 
factor under usual conditions. 

Professor M. Meyer has also recently made a similar study 
of the methods of grading at the University of Missouri. 
There appears, however, to be some contradiction or incon- 
sistency in his preliminary discussion, if the writer has under 
stood the matter at all rightly. In criticising and rejecting 
the proposal of Professor Hall, mentioned above, that the dis- 
tribution of marks should conform to the binomial curve. Pro- 
fessor Meyer presents the results of a test made by himself of 
the native musical ability of seventy-one students. The dis- 
tribution actually found does not conform at all to the bi- 
nomial curve nor to the probability curve, or, in the terms of 
the statistician, to the distribution of frequencies of the law 
of error, which Professor Meyer makes the basis of his pro- 
posal. The following statement of the case is made: 

"It seems plausible to start from the assumption that the 
combined mental and moral ability which we want to measure 
is distributed among different people in accordance with the 
probability curve, which describes, e. g., the distributions of 
accidental errors in scientific observation." It would seem 
that the reason ^Dhy it is plausible to start from this assump- 
tion, is that those mental tests and characteristics which lend 
themselves to more or less precise measurement, do. as the 
results of Galton, Pearson, Cattell. Thorndike, and others, 
show, conform fairly closely to this so-called normal distribu- 
tion. The native individual differences in various mental abili- 
ties tested, when the usual caution, as to a sufficient number 
of cases, sex, age, training, and selection, etc., is taken, appear 
to conform to the general biological law of variation nearly as 
closely as do the similar physical or anthropological measure- 
ments of height, weight, cephalic index, etc. Professor Meyer's 
tests of the native musical abilities on the contrary, appear as 
far as the number of cases measured is concerned, to be an 
exception to the general rule and by itself invalidate the 
assumption on which his argument is based. 

Marks, representing as they do, the teacher's estimate of 
mental abilities of various sorts, may themselves naturally, 
as noted above, be distributed according to the same fre- 



SCHOOL AXD UMVERSITY GRADES 17 

quencies as are the abilities wliich they are designed to repre- 
sent. We may find instances where this has been done, and 
Professor Meyer possibly does Professor Hall scant justice in 
failing to note in connection with his criticism of the latter's 
contentions, that, in spite of the unequal percentile units em 
ployed in the scale of marks, to which attention is called, the 
distribution of grades assigned by Professor Hall to some 
2,300 students, is a fairly close approximation to the probabil- 
ity curve. It is not, to the writer's mind, an important, al- 
though a proper, criticism, that the percentile units are not 
exactly equal amounts, since it is apparent that the main 
differentiation is made on the basis of the nine general grades 
employed; and it would probably make little difference in the 
actual grading, whether or not the percentile amounts of each 
grade are exactly the same, since the distinction into nine 
diffei-ent ranks is about as fine a scale as most can employ; 
and a finer differentiation usually does not mean much. 

These criticisms do not affect the validity of Professor 
Meyer's contention, but are concerned with what seems to be 
an inconsistency between the facts presented in the criticism 
of Professor Hall and his own proposal. It is fair to assume 
that marks may properly be distributed according to the fre- 
quency of the probability integral, because the individual 
differences in native capacity are according to most studies 
approximately so distributed. 

Such a distribution of marks as has been proposed finds, 
therefore, justification both from theoretical considerations, 
and from the fact that it is used in actual practice. Several 
proposals have been made in regard to the division of the dis- 
tributions into groups corresponding to the usual grades of ex- 
cellent, good, fair, poor, and failure. What proportion of stu- 
dents should be found in each grade, assuming that their 
marks are to be distributed according to a normal distribu- 
tion? If we divide the base line of a theoretical curve into five 
equal parts in order to secure the same range of abilities, we 
should secure the following percentages in each grade in a 
normal distribution: 

A B C D E 

Excellent Good Fair Poor Failure 

2% 23% 50% 23% 2% 



18 



THE UNIVERSITY OF WISCONSIN 



This distribution is shown in the upper distribution of 
Figure 8. Figure 2 of Cattell. '•" 




Professor Cattell believes a somewhat different distribution 
more convenient for practical use, as indicated in the following 
quotation from his discussion: "" 

"If the performances of students in examinations are as- 
sumed to vary in the same way as their height, then we can, 
if we like, place them in classes which represent equal differ- 
ences. Thus by the Harvard-Columbia method of grouping 
into five classes, if we put half of the men into the middle 
class, C, and let B and D represent an equal range, we should 
have about 23 per cent of both B's and D's and about 2 per 



<^> Popular Science Monthly. 66: 372. 

<«> CsLtteU, Examinations, Grades and Credits in Popular Science Monthly 
66: 371 seq. 



SCHOOL AND UNIVERSITY GRADES 19 

cent of H's and F's. This, however, gives too few men in the 
H and F classes for our purposes. If we make the range of 
the unit 20 per cent smaller, we obtain the distribution shown 
in Figure 3, (reproduced in Figure 8, lower chart), according 
to which of ten men four would receive C, two B, two D, one 
H. and one F. It departs slightly from the theoi-etical dis- 
tribution but certainly not so much as the theoretical distribu- 
tion departs from the actual distribution. It appears to be 
the most convenient classification when five grades are used; 
one in ten being given honors, and one in ten being required 
to repeat the course, corresponding fairly well with the average 
practice and being a convenient standard." 

The following table and figure showing the grades given 
to 200 students in each of five courses in Columbia College 
furnishes another example of the fact that the general average 
of grades usually approximates the theoretical distribution: 

Percentages of Students Receiving 

A B C D E 

English A 4.5 41.5 44.5 4.5 5. 

English B 4. 40. 39. 6.5 10.5 

Mathematics A 11. 24. 24. 22. 19. 

History A 10.5 28. 28.5 20. 13. 

Economics A 9. 36. 33. 17.5 4.5 

Average 8. 33.9 33.8 14.1 10.4 

The variations in the separate subjects will be discussed in 
Chapter IV. The following statement is made by Professor 
Cattell : 

"The average grade is a little above C, the median grade is 
nearly midway between C and B, and more than two-thirds of 
all the grades are either C or B. Eight per cent of the grades 
are A and 10 per cent are F, which approximates closely to the 
standard recommended above. The average of the grades 
assigned in these courses does not vary considerably, but the 
distribution is different. In the courses in English the dis- 
tribution tends to follow the normal curve of error, with the 
failures as a separate group or species. In the courses in 
mathematics and history the groups are more nearly equal in 
size, except in the case of excellent. Here the range of ability 



20 THE UNIVERSITY OF WISCONSIN 

is presumably greater in D and F than in B and C. The dis- 
tribution in economics is intermediate. The fact that the 
courses in English, though given by different instructors, corre- 
spond closely, shows that within a department certain stand- 
ards may be followed; and that this would be possible for the 
whole college or for the educational system of the country. It 
is only necessary to adopt the standards and then to teach peo- 
ple how to apply them." '"* 

Professor Meyer in the discussion '^' of the grading of 
pupils in the University of Missouri, just mentioned, argues 
for the use of the theoretical distribution, and the division 
into three grades, the median grade containing 50 per cent of 
the whole group, the remaining 50 per cent being divided 
equally into the grades of superior and inferior students. As 
regards further subdivision of these groups, the following quo- 
tation may be made from his discussion: » 

"We have divided all students taking a particular kind of 
work into three-groups, medium students, inferior students and 
superior students. Should we subdivide these groups? 

"Little can be said in favor of subdividing the medium 
group. That this group is the largest, is, in itself, no reason 
for subdividing it. A strong argument against subdivision is 
the fact that this would bring about unjust grading of a large 
number of students. The curve is highest for medium ability. 
If we divide the area by a vertical line, we must have a large 
number of students on one side differing by an almost in- 
finitesimal amount of ability from a larger number on the other 
side. If the teacher, nevertheless, has to give them different 
grades, the probability is that a considerable number will re- 
ceive grades either too high or too low. This probability of 
injustice must be avoided as much as possible. It can be 
largely avoided if we make subdivisions only where the curve 
is comparatively low; and it is best, therefore, to give all the 
students within the central area of 50 per cent the same 
grade." "" 

"More advisable than a division of the medium group of 
students seems a subdivision in the group of superior students. 



Id. pp. 373-374. 
Science N. S., 28: 246-2.50. 
Id. p. 248. 



SCHOOL AND UNIVERSITY GRADES 21 

To belong to the group of the 25 per cent best is not a great 
distinction. It would be well, therefore, to separate from the 
group those wlio possess unusual ability. The manner of sub- 
dividing the group is a matter of convenience. We may pro- 
ceed in the following way. In the probability curve (Figure 
2) the point of extreme ability, where the height of the curve 
is practically zero, is chosen as 3. Tlie point of the vertical 
line which separates the superior from the medium students, 
is then .68, as can be read off from any table containing the 
values of the probability integral. It suggests itself to divide 
the ability-difference between this point and the extreme point. 
3, into two equal parts. The result of this division is the point 
1.84. To the left of this point are then found 3 per cent of all 
the students, as can again be read off from any table of the 
probability integral. We have thus divided the group into two 
parts in such a way that the best possible student is as much 
better than the best student of the second class, as this one is 
better than the best of the medium class. Let us, then, call 
the three per cent just separated by the name of 'excellent' and 
retain the name of 'superior,' for the 22 per cent following. 

"In the same manner we may subdivide the group of in- 
ferior students, calling the three per cent worst, 'failures.' and 
retaining the name of 'inferior' for the other 22 per cent. 

"I expect to meet with opposition when I restrict failures 
to such a small percentage. But I believe that three per cent 
is a sufficient number in order to weed out those who have suc- 
ceeded in entering college, but are entirely unable to do the 
work which they have chosen. I can not regard it as just to 
grade the other 22 per cent as failures. But I do not mean by 
this that they ought to be permitted to take advanced work 
in the same line of study, or to enter courses of other depart- 
ments for which this particular study is required, or that they 
should receive credit for the whole number of hours. The 
teacher who gives these advanced courses, and the teacher 
who gives the courses of the other department, must have the 
power to admit or to exclude these 22 per cent as he deems 
best. And the faculty should decide what fraction of the regu- 
lar number of hours of credit they should receive. Similarly, 
the faculty should, as Professor Cattell has proposed, give 
more than the usual number of hours of credit to those stu- 



22 THE UNIVERSITY OF WISCONSIN 

dents who have excelled the medium 50 per cent. To make 
all this possible the teacher must place each student in the 
group to which he belongs according to his rank. But those 
whose rank puts them in the fourth group should not be called 
failures in every possible sense — should not be regarded as 
having accomplished nothing. If a teacher instructs his class 
in such a manner that according to his own judgment 25 per 
cent of them accomplish nothing, then the conclusion is justifi- 
able that the teacher as a teacher has not accomplished any- 
thing, either." <^''* 

III. INEQUALITIES IN GRADING 

Having these facts before us, an examination may now 
profitably be made of distributions which do not conform to 
the theoretical curve and to the many resulting inequalities in 
the marking system. These examples are taken from a study 
of the grading in the University of Wisconsin and in several 
of the high and elementary schools of the state. We may begin 
with the latter, and with an example that is not unusual in its 
occurrence. 

There are two classes of the same grade, e. g., the seventh, 
in the same school taught by different teachers. The assign- 
ment of pupils to these rooms is made on purely incidental 
grounds, e. g., alphabetically, with no differentiation as to 
scholarship. The superintendent finds, however, that the 
marks assigned in one room average ten to fifteen points high- 
er than those given in the other room. In one class, half of 
the pupils receive grades above 85, in the other room half of 
the pupils are graded below 70. In such a case as this it would 
seem to be one of the functions of the superintendent or prin- 
cipal to find out what is the cause of this difference. Not in- 
frequently he may find that the fault is to be laid at his own 
door. He may discover that he has not made clear to the 
teachers either what the prevailing standards of marking are 
in his school or what they should be. Several causes might 
be assigned for the above difference. The pupils in one class 
are actually that much superior to those in the other class. 
This is possible but very unlikely under the conditions named; 

(lo^ Id. p. 249. 



SCHOOL AND UNIVERSITY GRADES 23 

it certainly would not be likely to happen twice in succeeding 
years. Secondly, one teacher is very much superior to the oth- 
er — is able to get more and better work out of her pupils, etc. 
The superintendent can ascertain whether this is actually the 
case; if it proves to be so, it is questionable whether such un- 
equal work on the part of teachers can be tolerated in the same 
school. Another explanation is that these are purely arbitrary 
differences in the standards of the marking used by the two 
teachers; one teacher is accustomed to mark all pupils low 
and the other to rate them all high; the teachers would or do 
not differ in their judgment as to what pupils do the better 
work, but simply as to the absolute mark to be assigned to 
them. This is a purely artificial difference, but it is also either 
in whole or in part the most frequent cause of the apparent 
inequality in marks. The same difficulty is found elsewhere. 
If we are considering one hundred pupils in each of two high 
school subjects, e. g., English and history, we may anticipate 
some slight difference from year to year, but in the long run 
there should not be any difference at all in the percentage of 
pupils who receive the same grades. For every pupil who ex- 
cels in English there will be one who excels in history, or in 
mathematics or in any other school subject. 

Are there not, therefore, certain rules which a superinten- 
dent may lay down, or certain suggestions which he may offer 
to teachers, in addition to the usual ones in regard to the rela- 
tive weight of the examination and daily recitations, in the 
making up of the total mark, etc? It is not enough to tell a 
new teacher that "in this school we mark on the scale of one 
hundred" (which, as a matter of fact, they seldom or never do, 
the scale usually being from about 50 or 60 to 100, frequently 
from 75 to 100, or in other words, on the basis of 25 to 50 
points of difference rather than 100). Nor is it enough to say 
"there are five grades 'A,' 'B,' 'C,' 'D,' 'E,' or 'Ex.,' 'G,' 'F,' 'P,' 
and 'Failure,' and if you think a pupil's work is good, give 
him the grade 'G.' Is it a perfectly proper question to ask 
what is good in this school? And one of the best answers 
which can be given to that question is to indicate the percent- 
age of pupils who from year to year attain that grade. 

In view of the considerations in the preceding sections, it 
would be well if a principal could say to a new teacher: "In 



24 THE UNIVERSITY OF WISCONSIN 

most of our classes, taking them year after year, about one- 
half, or 50 per cent of the pupils, secure the grade of 'F' and 
about 25 per cent of them get above that grade and 25 per cent 
of them below^ it. Of course in any individual case there will 
be variations from year to year especially in small classes, but 
if the teacher puts together the grades assigned to him for 
several years back there should be a very close approximation 
to this result, and at any rate the marks of all the teachers in 
this school when taken together for any given month or year, 
give, in general, this result." This gives some fairly definite 
notion of what the grade "F" means in this school. 

If the superintendent, instead of adopting standards some- 
what in accord with the theoretical requirements, wishes 
simply to maintain more uniformly the standard actually 
prevailing in his school and not attempt any great change in 
the system as he finds it, it is more likely that his statement 
will need to be: "In this school we find that taking into con- 
sideration the grading of all the teachers, about 60 per cent of 
the pupils secure grades of 'good' or above. About 20 per cent 
secure the rank of 'excellent.' about 40 per cent the rank of 
'fair' or below, and about 10 per cent the grade of 'poor;' and 
one or two per cent fail. We wish to make this the general 
practice." Such a definite understanding would make for 
uniformity in the marking system. There will be exceptions, 
some of which are discussed below, but this proposal is better 
than leaving it to the individual teacher to decide for herself 
not simply as to which pupils are the better pupils — which 
it is her business to determine — but to determine that no pupil 
in her classes, however good, shall receive a grade higher than 
95 when the teacher in the next room employs the grade of 99 
and 100, or to give the poorest pupil a rank of 40 when an- 
other teacher would use 60, or to grade half of her class "good" 
when another teacher having the same pupils to deal with 
assigns to half of them the grade of "fair." 

Another example may be instanced which might well re- 
ceive the attention of the principal or superintendent. When 
marks are assigned according to the principles which have 
been discussed above, we should not only expect to find rela- 
tively little variation from year to year in the same class or 
grade, but the distribution of marks in the various grades in 



Tvgure 3, 

6^ /Pupils of the E/ahth Grade 

X xxxxx X XXX x;^x 

^ }^^6 X XXXXXXXXX XXXXXXX X K 

S3 Pujails cfthe i Sewenth QradQ 

t1edm=83 M ^ x ^ >. »,x>x 

^X X A?CX X. X X X XA JfX^^X 

66 Sixtjf) Grade Rjpils x x 5 

nedm-Sg » » x^^ x J Jx J J x x 

*^X X xxxx> )(xJrxxxx xxx x x 



{ 



9^ PuD/Zs cftk Fihh Grad^Q | 

X XX X X XX X 

X X xxxxx X AX X V, / „^ 

^ ><yXXXX> X XX X >< X XX 



SSfoudh Brade Pvjoils j I 

X XX X XXX 

X XX X i XXX 

X )< X XX XX XX xW 

JUJ/upils of the Thrd Grade xJ 
Med/aio=86 X >«lf^x 



A XA ^ X x/xxxxxxx 

X XX.X ^ X A X xxxxx xxx: 



^ 'f'f*,^ w.^ X X xxxxxxxxx^^ 



26 THE UNIVERSITY OF WISCONSIN 

school from the lowest to the highest school should not vary- 
materially. If there should be any difference, we might expect 
to find, as we advanced through the grades, a somewhat higher 
percentage or frequency of high grades because the poorer 
students fall behind or drop out of school more frequently 
than do the better students. In order to see in how far this 
is true in practice, I have plotted on the following pages the 
standings of a group of students from the third to the eighth 
grades, inclusive. This has been done in two different cities, 
A and B. The following simple method of plotting has been 
followed, in the horizontal scale of marl<s crosses have been 
placed above the proper percentage to indicate the rank se- 
cured by the several students. The marks are the ranks in 
English in the various grades. (See Figure 9.) 

The groups in either case are composed largely of the same 
students throughout, although occasional students who entered 
after the third grade are included. That there are fewer stu- 
dents in the distributions of the last three years than of the 
first three is, of course, due to the dropping out of school of 
many pupils. The charts represent, therefore, in the main, 
only those students who entered the third grade in the year 
under study and remained in school, and whose complete rec- 
ords could be found. Under such circumstances then, we 
should not be prepared for such results as appear on compari- 
son of the third and fourth and following grades of school A. 
In this case, promotion for these pupils means that the major- 
ity of the class receive somewhat poorer marks than they se- 
cured in the lower grade, and for a number a very consider- 
able lower standing. Since the poorest students have doubtless 
fallen out, the pupils might, if anything, expect somewhat 
higher ranks. The explanation that the class was not pre- 
pared for fourth grade work can not be accepted when the in- 
stance is of frequent occurrence. The work should be adapted 
to the class under these circumstances and not vice versa. 

In Figure 10 similar distributions are given of the marking 
in the grades of a grammar school in another city. The varia- 
tion in the number of pupils is due to causes which need not 
be discussed, but a sufficient number of pupils are carried 
through to make the results of some significance. The seventh 
and eighth grades are combined in one class. The tendency 



SCHOOL AND UNIVEKSITY GRADES 27 



f7(jure JO 

8^ Pupils of the Sewemth md Eighth G fades 
X ^ XX X xxxxx;<X/^ 

X X X^^<^^^'>^ ^ XXXXXXXAX/K ?^ A 

XX y X gy yScxxxxxxx^xxxxxxxxxxAxx x 

ho (>S 70 7S So 8S ^ IS 




ioH Sixth Grade Pupik. 

;xxxpx 
, X ?S, xxxxxxxx'x^cJcxx^xxx 

6i) 6S Id t ^ 65 1o is 

tiGclm==y7 S7/^oyrU Grade Ri/o/ls 

X ;< X XX 

^ X X^ XX X xxxx X 

XXXX XX xx;<xxx X xxxx X 

XXX XX XX xxxx^;<xxx xxxyxAXX 

bo 65 7<9 7^ 80 8S 9o % 



28 



THE UNIVERSITY OF WISCONSIN 



in this school to raise the marks of the succeeding grades is 
more defensible than the practice of the other school just 
mentioned. 

The preceding examples have been taken from the gram- 
mar schools, while the following cases are from the high school 
and university. Figures 11-14, inclusive, show several dis- 



ru 



n 



English ^ 83 iUjoiIs 

r-| Mec^ian-80 



X 7o7/ )^ m >7^ % yjf 7i'!^8bBJ 8S 8i> 8^ 8S 8(, 87 88 8f ^d i/ n 717^ 



-B. 



tlediayi^SO 



t^^ 



Matheivatics^78Jiipils 



r^r-L,r^ 



X 707/1 Of^ 757j^7S7i>7J^y87f 8o8t 82 8i8i^8S 86 8!^88 899o 9J 9!^ 91 S^ 2s 36 3^98 
High School grades of same pupils in English and Mathematics 

tributions of grades in high schools and university, which are 
open to many points of criticism. In Figure 11, A and B are 
the distributions of practically the same pupils in high school 
classes in English and mathematics. It does not appear likely 
that as a groxip there should exist such a difference in the 
abilities involved in these two school subjects as seem to be in- 
dicated by the marks given. It is a condition due to a merely 
arbitrary difference in the standards of the teachers con- 
cerned. 

Chart 12 is a distribution of a class in freshman mathe- 
matics. In this case the relatively large number who receive 
the grade of 70, tends to make the distribution of marks in the 
other grades very unequal. A range of over 30 marks is em- 
ployed, seeming to indicate that degree of differentiation, 
whereas, as a matter of fact, no differentiation is made in the 
case of nearly one-third of the students graded. 

Charts 13 (a and b) and 14 (a and b) show the distribu- 



1 1 ; 

Ml 1 


_i- 4- 4-1- ^^ 


Till 11 


-ir ■^' 


1 ; 1 ■ 1 


— S-J J 1' 




========--1=====^^^ 1^ 


— 1 — — 1 — — 1 — — 1 — — \ 


"T- = : S; 


; Mill 1 

Ti — r "1 — 


^ . ....... -,„ J 


1 M ^ ' 1 1 
1 1 1 

1 M 1 1 i 1 ' " ^ 
1 — \"J~\ t M ' 




1 1 1 1 1 1 T ■ ■ 


f f----""-^"l i 


i 1 ' ~^ 

Ml 
1 






+ j:i ± : ^1 

ff 'lllftTliMffli 
I, iiiiinina4 




._± .^1 

:=Ft:ii-2=i::-:ii:: t. 



>r/g.y3-/7. 



nOnriJ 



1 



\A^ 



fyti Corii 707Jj^l5M%'J^78:&SO&f;^8lBfiSSkei8»990^l^^^l^^S%^;8f9 







jFVd Con'd 70)l)niWS%7V82fScSi8^8imiSb8JSS8^70»^^7i3ih?s;n>%lJi8:if 






FTd ComV 7o7in7i7n27an8j^^&ihnuid^s^sm^oj(/jm^fj^^!i.fffH 



II 



fl,J')--B. 



J oji^ri [UL^ V 



jFTd CohV 7^7^7^M}^M/S2^^9/S^S58/8SSl,&889/'^/^/i/J';ai^/;8 



SCHOOL AND UNIVERSITY GRADES 31 

tion of grades in the case of about equal numbers of students 
from the College of Engineering and the College of Letters and 
Science of the University of Wisconsin in two freshman sub- 
jects, — English and mathematics. The chart makes possible, in 
the first place, a ready comparison of grades given to two 
different classes of students of engineering and of letters and 
science; and, in the second place, of the grading in two typical 
freshman studies. In the first connection it is interesting to 
note that there is always danger of considerable error, when 
persons attempt to make comparison of large groups of in- 
dividuals purely on the basis of general impressions. 

It seems to be the prevailing impression, for example, that 
the engineering students at the university do much poorer 
work in the study of English than do the students of the Col- 
lege of Letters and Science. This, as the chart indicates, is 
to some extent true, but not to the extent that is commonly 
believed. In such cases as this, the general impression is apt 
to be unduly influenced by the extreme cases, e. g., by a some- 
what larger proportion of inferior or poorly qualified students. 
In making comparison of large groups, some statistical method 
is almost always requisite in order to secure an accurate state- 
ment. 

The large percentage of failures and conditions given 
in the freshman engineering mathematics, is apparently a 
conscious attempt at the elimination of the poorer students on 
the basis of the standings in mathematics. This is a higher 
percentage of failure than is usually justifiable, provided that 
only properly qualified students are admitted. The conclusion 
would seem to be that either students, who were not properly 
prepared or qualified, were admitted to the work, or else the 
grading is somewhat unfair. The practice of admitting a large 
number of students and selecting the more efficient is, of 
course, a method which has many advantages, as well as dis- 
advantages. The more frequent fault of the system is that the 
standing in one subject, — not infrequently mathematics, — is 
apt to be made the chief basis of elimination. "While it is true 
that the general average of viost of the students who are drop- 
ped from the university is low, — although this is by no means 
always the case, — this result is in itself sometimes due to the 
greater demands made on the student's time by the subjects in 
which he is deficient. 



32 THE UNIVERSITY OF WISCONSIN 

The second comparison suggested by Charts 13 A and B and 
14 A and B is, perhaps, the more important. The differenci? 
in the grading of students in English as compared with mathe- 
matics is very apparent. The distributions in English tend to 
be "normal" with the larger proportion of students in the 
median grades. In mathematics there is a clear tendency to 
group students as either "good" or "poor" with relatively few 
■of "average" ability. This, as pointed out elsewhere, is prob- 
ably not a true representation of the facts. 

In these charts, as well as in several which precede and 
follow, a marked tendency to use certain grades in preference 
to others is evident, as, for instance, the division of five, viz., 
70, 75, 80, 85, and 90, and, in the university grades, the turn- 
ing points of the grades, as 78, and 93, as well as some other 
marks, as 88. This coupled with the fact that certain grades 
are correspondingly little used, or in some cases practically not 
at all, seems to indicate that the actual range of marks here 
employed is greater than can be used with discrimination. 
Teachers either cannot or will not differentiate to the extent 
of 25 to 30 points in the work of the students of a class. The 
fact that one teacher marks 80 and another 83 is largely a 
matter of individual predilection. Ten to twelve degrees of 
differentiation is the maximum that most can employ with 
any meaning, and it would, on the whole, cause greater uni- 
formity and less inequality if that was all which was at- 
tempted. The use of five grades, with possibly a further dif- 
ferentiation of a plus and minus in each grade, would really 
be a more accurate method than a somewhat random use of 
30 apparently more precise grades. The latter is apt to lead 
to careless marking, and apparently greater differences of in- 
dividual judgment between teachers than may actually exist. 
Probably no particular harm is done, but teachers are deceived 
into thinking that they are securing much greater precision 
than as a matter of fact results when the system as a whole, 
rather than any one individual's grading is considered. 

Another fact that sometimes leads to inequalities in mark- 
ing is that students in advanced courses are apt to be graded 
higher than in elementary courses. Chart 15 gives the dis- 
tribution of the standings of 175 students in an advanced 
•course in English Literature. The average is. as may readily 






Zr 



j^ 



? 



a 



4 



^ 



§ 






ri 



§ 



1 



vi 



c 



ES 



34 THE UNIVERSITY OF WISCONSIN 

be seen, much higher than in the case of the freshman class 
just cited. There is no reason, as it seems to the writer, why 
this should not be the case, but it not infrequently leads to 
inequality chiefly because individual instructors do not realize 
that this is the general practice. 

Professor Meyer has raised certain points in the article 
already referred to that bear upon this fact. One justification 
for this high grading of students in the advanced course, may 
be made on the basis that the students are a more selected 
group. 

Professor Meyer does not attempt, in the short article re- 
ferred to, any discussion of this somewhat involved question. 
There is, as yet, little evidence as to what extent the selection 
of the university makes for the higher grades of ability. 
There has undoubtedly been considerable selection operative 
as between the lower grades of the grammar school and the 
university, but it is doubtful if there is very much difference 
in this respect between the university and the high school. <^> 
It would be attempting much more precision than the grading 
of pupils is ever likely to attain, to take much account of this 
factor in its general aspects. The question does arise, how- 
ever, in another form, namely, whether, in some instances, 
superior students do not elect certain lines of work or in- 
dividual courses, and that at the same time these courses are 
avoided by average or inferior students. 

If there are such cases, the grading should be higher in 
these latter courses. The trenchant criticism of Professor 
Meyer in this connection is quite to the point, however. The 
high grading is more often due to too great leniency, etc., on 
the part of the instructor than to the presence of superior stu- 
dents in his courses. Teachers sometimes, too, appear, as 
Professor Meyer states, "guided by the conviction that the very 
fact of a student electing his work under his instruction proves 
that he is a superior student and that he ought to obtain high- 
er than the average grade." 

Still I question whether the proposal that "If a student ex- 
cels, this means, of course, that he excels among the students 
who are taking the same instruction which he is taking," can 



*Por some data on this question, see an article by the writer on 
"Qualitative Elimination from School," Elementary School Teacher. 
Sept. 1909. 



SCHOOL AND UNIVERSITY GRADES oO 

be universally applied. While they may be exceptional, it vi^ill, 
I think, be generally recognized that there are usually some 
courses in a university which, from year to year, secure only 
an inferior grade of pupils, and other lines of work which, for 
various reasons, secure a disproportionate number of superior 
students. Classical students in the high school and university, 
and students in the advanced courses in mathematics are often 
examples of such selected groups of students. The above 
principle would not be equitable in these cases. 

A more important exception occurs in the case as just 
noted, of all advanced courses as compared with elementary 
courses. In the University of Wisconsin students in advanced 
courses are graded about 20 per cent higher than in the el«:^ 
mentary courses. Juniors and seniors are similarly graded 
much higher than freshmen and sophomores. This practice 
holds consistently for all departments as a whole and for most 
individual instructors, and since the prime requisite for equi- 
table grading is uniformity, I see no reason, as just stated, why 
an attempt should be made to change the arrangement and to 
secure the same distribution of marks in the advanced courses 
as in the elementary. 

There are, on the other hand, many reasons why the ar- 
rangement is a natural one. In the first place many students 
have been dropped from the university during freshman and 
sophomore years. Those who remain are presumably on the 
whole better qualified to meet the university requirements, 
and might naturally expect to receive at least as high grades 
as before. If the student were graded as Professor Meyer 
suggests, solely on the basis of the relative rank he attains 
"among the students who are taking the same instruction that 
he is taking," some students must because of the elimination 
of the poorer students, receive lower grades than they did in 
the elementary courses. They presumably have in many cases 
elected the advanced courses because of interest or success in 
the elementary work. Students in the advanced courses have 
thus been more or less sorted out and differentiated as regards 
their interests and abilities, and are undoubtedly as a whole 
better qualified for their work. There is no reason why they 
should not on this account be graded higher. 

In estimating, in a following section, the extent of in- 



36 THE UNIVERSITY OF WISCONSIN 

equality existing among the various instructors in the uni- 
versity, I have, therefore, taken account of this factor. If one 
instructor has a larger percentage of advanced students than 
another, it may be expected that he will give a larger percent- 
age of high marks. Since this is the prevailing practice, no 
inequality results. The results of Professor Meyer in regard 
to the University of Missouri may very possibly on account 
of this factor, represent a larger extent of inequality than in 
reality exists. 

Furthermore, in the case of any given class it may be 
approximately determined whether or not as a group the stu- 
dents do differ much from the average, by finding out whether 
they rank similarly in other subjects of study which they are 
following. Mental abilities are certainly not so specialized 
that any considerable group of men are found doing superior 
work in one subject, who will not take somewhat similar rank 
in other subjects of university instruction which they may also 
be following. 

IV. GKAllES IN DIFFERENT SCHOOL SUBJECTS 

It was stated above that we had reasons to believe that the 
distribution of grades in different subjects should not be un- 
like. Many instances from the ranking of pupils in the high 
school and university might be presented where this is the 
case. The distribution of marks in such subjects as history, 
German, English, and mathematics, should, when a fairly 
large number of pupils is concerned, ordinarily be similar. 

It may be assumed that in general a hundred or more stu- 
dents in one course do not differ as a group much in general 
intelligence or in their ability to succeed in given subjects 
from a hundred students in another subject. Some courses or 
lines of study may select superior students, and others inferior 
students, but these are the exception rather than the rule, 
and may be dealt with as suggested in the last chapter. We 
may expect then that the grades or marks assigned to a large 
group of students in different subjects of study will be similar, 
and that they will be distributed in the various grades in 
about the same frequencies. Some instances, both of where 
this is true and of where it is not true, will be cited below. 

In order to recall to mind the close relation which fre- 



SCHOOL AND UNIVERSITY GRADES 37 

quently exists between the distribution of ttie marlis of a large 
group of students and tlie normal distribution, tliis comparison 
is made in Figure 16. Tliis shows a distribution of 244 pupils 
in high school English. Its approximation to the normal dis- 
ti-ibution is indicated by the dotted line. Figure 17, on the 
other hand, shows a distribution of the standings of 146 stu- 
dents in freshman mathematics. It varies widely from normal 
distribution as indicated by the dotted line. Both for the 
theoretical reasons outlined in a previous chapter, and because 
of the fact that the sort of distribution shown in Figure 16 
is closely approximated in the majority of cases of grading, it 
should, as it seems to the writer, be taken as the standard. 

If, then, a large group of students are graded as a group 
very differently in two school subjects,- — as in the case of 
English and mathematics cited in the last paragraph, — we shall 
consider that distribution more nearly right which approxi- 
mates the so-called "normal" distribution as seen in Figure 16. 

Figure 18 presents another example of this sort of varia- 
tion which exists in the grading of the different school sub- 
jects. The continuous line of the chart shows the distribution 
of the grades of 79 pupils in the sophomore year of a high 
school class in English. The dotted line shows the distribu- 
tion of the grades of the same pupils in a class in mathematics 
taken during the same year, (74 pupils). It is hard to believe 
that as a group the class would differ in the way indicated. 

Figure 19 gives a similar comparison of the standings of 
university freshmen in German and histoi-y. The groups are 
made up of practically the same individuals, (226 freshmen). 
Although there is a tendency to grade a considerable number 
of the pupils in German higher than in history, as a whole the 
two distributions are not unlike. This, as just stated, should 
be the case. There may be a definite reason for the higher 
grading of some pupils in German due to the fact that the 
freshman class is composed both of those who have had con- 
siderable preliminary training and those who have had none. 

In Figure 20 a similar comparison is made of the stand- 
ings of 218 pupils in history and mathematics. These are 
all practically the same students as were compared in Figure 
19. The difference here between the form of distribution be- 
tween history and mathematics is more striking. Since the 



38 



THE UNIVERSITY OF WISCONSIN 



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THE UNIVERSITY OF WISCONSIN 



distribution in the case of history is much closer to a normal 
distribution, it must, for the reasons given above, be consider- 
ed the better distribution. As noted above, it would appear 
that there was a tendency in the case of the classes in mathe- 
matics to consider pupils as either good or bad; there is less 
halfway ground, or in other words, fewer medium or mediocre 
students than in other subjects. It is hard, however, to be- 
lieve, as said above, that, as a matter of fact, the mathematical 
abilities are distributed any differently than others. These 
apparent differences must, as it seems to the writer, be largely 
attributed to artificial methods of grading. Some further facts 
in this connection are discussed in the succeeding chapters. 



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SCHOOL AND UNIVERSITY GRADES 



43 



V. THJE UNIVERSITY GRADES 

The following charts show the actual distribution of the 
averages of the grades attained by students in the first two 
years of the university, (Figure 21), and in the last two years, 
(Figure 22). There are about 5,500 averages plotted in Figure 
21 and a little less than 6,500 in Figure 22. These marks are 
combined in Figure 23, giving' a total of about 12,000 general 
averages. In these cases all the marks of a student in the 
chief subjects of instruction, were, in each case, averaged. The 
marks taken were given in three different semesters and they 
may, therefore, be considered as representing what is the gen- 
eral standard of grading in the university. In order to remove 
the irregularities in the disti'ibution of Figui'e 23 which are 



J30- 



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44 THE UNIVERSITY OF WISCONSIN 

due simply to the predominance of certain grades as 85, 90, 
and 93, the grades have been regrouped in Figure 24 under 
ten divisions as there indicated. Ten, as noted above, are 
about as many grades of difference as usually have much sig- 
nificance. This procedure results, as may be seen, in a dis- 
tribution which is "heavier" in the higher grades and not 
"balanced" about the median point as in the case of a normal 
distribution. This fact is mainly due to the higher grading of 
the junior and senior years, as compared with the first two 
years. This difference in the first two and, last two years of 
the college course may be seen by comparing Figures 21 
and 22. 

If, as Professors Cattell and Meyers have suggested, the 
high schools and colleges would publish occasionally, or dis- 
tribute to the members of their faculties, some such record of 
the actual practice of marking in the institution concerned, 
as is here given, this in itself would tend greatly to promote 
uniformity in grading. 

For further comparison, the j^ercentages of marks assigned 
to the five divisions employed, — excellent, good, fair, poor, and 
condition or failure, — is also given in the following table. 
Those conditioned or failed have been put into one group. 
Column 1 gives the percentages for the freshman and sopho- 
more years, 2 for the junior and senior years, and 3 for all 
four years. 

Percentages of Grades Assigned in the University 

No. of 

1 Freshman and Ex. Good Fair Poor Failure Cases 
Sophomore 13.8 33.2 28.7 16.8 6.9 5494 

2 Junior and 

Senior 18.3 44.7 24.2 9.G 3.2 6397 

3 All four years.. 15. 9 39.5 2G.4 13.3 4.9 12278 

In order to show the variations which exist between de- 
partments and individual instructors within the university, 
which have been arranged in the above distributions, tables 
are given in an appendix of the grading of various depart- 
ments and of the instructors in them. The synopsis given in 
the following tables of this chapter is sufficient to indicate the 
general extent of this variation. 



SCHOOL AND UNIVERSITY GRADES 



45 




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or 



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^ 









46 



THE UNIVERSITY OF WISCONSIN 



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'TT i ' MniTHl iI 



n Zodp- r+f- f* G-cff E- E+ 



SCHOOL AND UNIVERSITY GRADES 47 

The following table gives the range, i. e., the maximum and 
minimum percentages of the various grades assigned by in- 
structors in six departments during freshman and sophomore 
years. The range is larger in the last two years: 

Range of Marks Given in Single Departments 
(Freshman and Sophomore Years) 

Ex. G F P X 

max. min. max. rnin. max. iiiin. max. min. max. min. 

History 16.7 3.4 52.9 25.2 3S.9 27.3 26.S 2.3S ILS 

English 19.3 1.98 53.9 22.6 45.5 19.3 38.7 7.69 10.2 

Mathematics 24.1 12.1 27.8 18. 28.5 15.7 27.4 14.25 23.3 L29 

French 23.9 14.5 43.8 24.2 27.5 21.4 27.4 7.5 9.67 2.31 

Latin 26.1 11.7 47.6 46. 26. 15.9 16. 7.48 8.04 

German 34.3 14.47 49.1 27.4 33.5 19.4 22.95 2.98 10.95 2.27 

A simple method of presenting this variation in grading is 
to compare for each instructor the percentages of the first two 
grades — "excellent" and "good" — with the percentages of the 
remaining grades given. This comparison, for the reasons 
given in the last chapter, should be made separately in the 
case of the first two and last two years, since, as there stated, 
the grading of the last two years is uniformly higher than is 
the first two years. Considering the general averages of prac- 
tically all the marks given in the three semesters under study, 
(see following table), 47 per cent of the marks given in the 
freshman and sophomore years, and 63 per cent in the junior 
and senior years are either "excellent" or "good." Consider- 
ing the four years together, about 54 per cent of all the marks 
given are either "excellent" or "good," and but 46 per cent are 
of the remaining grades, "fair," "poor," and "condition" or 
"failure." This may therefore be considered the general prac- 
tice, and those instructors grading most closely to this aver- 
age, are under normal conditions grading most fairly. 

Percentages of Grades Assigned in the University 

(1) The sum of "excellent" and "good." 

(2) The sum of the remaining marks, i. e., "fair," "poor," 
and "condition" or "failure." 

(1) (2) 

Freshman and Sophomore 47% 53% 

Junior and Senior 63 37 

All years 54 46 



48 THE UXIVERSITY OF WISCONSIN 

In the following table the percentages of "excellent" and 
"good" of the whole number of marks given are presented for 
several departments. The two highest and the two lowest 
percentages for each department are given, the results of the 
first two years and the last two being stated separately. More 
detailed comparisons may be made by referring to the tables 
in the appendix. 

As has been shown in the above charts and tables, the per- 
centages of high grades is higher than should be found if they 
were distributed according to a "normal" distribution. The 
largest proportion of grades according to this system should 
l3e of the grade "fair." 

In the university more grades of "good" are given than of 
■"fair." There can be no important objection to this practice 
provided it is somewhat uniformly followed; but, if one in- 
structor believes that the majority of his students should re- 
ceive simply the grade of "fair" for the same work for which 
the majority of instructors will assign the grade of "good," 
inequality, of course, results. For this reason it is consider- 
ed that some knowledge on the part of all instructors of the 
general practice in the matter of grading will promote greater 
uniformity. In the case of the university grades, it has al- 
ready been noted that the students in the last two years are, 
as a general rule, graded considerably higher than those in 
the first two years of the university course. This is largely 
a, difference between "advanced" and "elementary" classes. 

The Two Highest (a and b) and the Two Lowest (x and y) 

Percentages of the First Two Grades (Excellent and 

Good) Given by Instructors in the Same 

Departments 

A B 

Freshman and Sophomores Juniors and Seniors 

abxyabxy 

English 67.5 62.9 35.2 31.6 80.4 74.3 52.4 39.0 

History 69.1 63.7 31.2 25.4 77.7 75.8 47.3 33.3 

German 74.6 63.6 39.7 30.5 77.5 76.7 60 52.8 

French 65 61.3 47.5 38.7 85.6 74.5 60 58 

Mathematics 49.1 44.4 ... 30 76.6 73.4 66.1 52.1 

Latin 73.7 62.1 . . . 57.9 78.9 78.0 73.5 65.9 

Philosophy 74.3 52.4 46.7 40.2 






^ 
SS 






74.7 


62 




53.1 


89.2 


71.3 


52.4 


39.0 


83 


66.2 




62.5 


85.5 


71.4 




61.1 


84 


65.1 


51 


36 



SCHOOL AND UNIVERSITY GRADES 49 

Education 

Political Economy 
Political Science. 

Physics 

Chemistry 

VI. THE CORRELATION OF SCHOOLS AND SCHOOL 
• SUBJECTS 

It was noted in Chapter IV, in discussing the grades in dif- 
ferent school subjects, that there should normally be approxi- 
mately about the same sort of distribution where there are 
large groups of students concerned. This, of course, does not 
mean that any given student will necessarily hold the same 
relative position in the different subjects, but simply that the 
distributions as a whole will be similar. The question of how 
widely students' work differs in various subjects is itself an 
interesting problem, although it is only indirectly involved 
here. Its bearing was suggested in the last chapter in dis- 
cussing the question of the election of courses by students. 
The following charts on Plate I indicate something of this 
relationship in the case of high school subjects, and are pre- 
sented here largely to indicate a simple method of study by 
which such a problem may be approached. The method used 
is as follows: 

All the pupils in the class are numbered consecutively. 
These numbers are then distributed on the scale of grades as 
seen in Plate I, Chart A, which shows the standings of 113 
high school pupils in Latin. Nos. 1, 7, and 2. above the grade 
94 signify that the three pupils indicated by these numbers 
secured the grade of 94 in their class work in Latin. The 
numbers of the first quarter of this class i. e., of those whose 
rank places them in the highest quarter, are then colored red. 
Those in the second quarter are colored purple; those in the 
third are colored green; and those in the fourth or lowest 
quarter of the class are colored black. These colors are re- 
tained in the distributions with which this is to be compared; 
that is, the colored numbers of these pupils are now dis- 
tributed according to their standings in English and mathe- 
matics. If they all received exactly the same grade in these 
two subjects which they received in Latin, there would be no 
change in the color relations; all the "reds" would be in the 



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1)2 Pupils 



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50 THE UNIVERSITY OF WISCONSIN 

first quarters of the classes in mathematics and English, as 
they were in the first quarter of the class in Latin and so on. 
A red colored number in another quartile than the first in- 
dicates therefore at once the fact that although this student 
was in the first quarter of his class in Latin, he does not stand 
as high in these other subjects. The amount or extent of such 
change will give, therefore, at a glance, the general correla- 
tion of standings in the case of these three subjects. There is, 
as was to be expected, some interchange of position, but in gen 
eral it is readily apparent from the chart that those who 
stand well in Latin tend to do very nearly equally as well in 
the study of English and mathematics, and on the other hand, 
those who are the poor scholars in Latin are apt also to be 
poor in their other subjects. Some exceptions, of course, ap- 
pear. Nos. 80, and 91, for example, rank in the first quartile 
in Latin, but are in the lowest quarter of the class in mathe- 
matics; but these are the exceptions, the rule in this particu- 
lar school at least, being a rather close correlation of stand- 
ings in these subjects of study. 

A similar problem of interest for the study of which the 
grades of pupils may be made use of is the relation between 
standing or rank of pupils in high school and their relative 
rank in the university. '^' A test in this way may be made 
of the success of the method of accrediting schools as a basis 
for admission to college. Such a study might also be of value 
in determining the closeness of relation between the work of 
pupils in the various grammar schools of a city and that done 
by them later in the high school. Such a study would furnish 
the best evidence of the efficiency of the various schools con- 
cerned, at least, in so far as preparation for the high school 
is a measure of efficiency. 

As a further example' of this method of study, there are 
presented in Charts 25-28 inclusive, the general distribution 
in the high school and the university of a group of 174 stu- 
dents who entered the College of Letters and Science from the 
Madison high school during the years 1902-1905 inclusive. In 
Figure 25 the dotted line represents the distribution of the 
general averages of these students in all their high school 



<i> This problem has been studied In detail in Bulletin No. 312, 
Hig-h School Series No. 6 of the Bulletin of the University of Wisconsin. 



SCHOOL AND UNIVERSITY GRADES 51 

work; the continuous line indicates liow they stood in the uni- 
versity. Their ranlvs, were, as may be seen somewhat higher, 
although this is an arbitrary difference of not much impor- 
tance. In Figure 26, the comparison is made between their 
ranks in the English studies of the high school and their rank 
in freshman English. The average, or median of the two 
groups, is practically the same (Medians^83.4 and S3. 5). 
Figure 27 shows a similar comparison in the case of German 
for 125 pupils. The freshman grades assigned these pupils 
average very much higher than the grades which they re- 
ceived in the high school. Finally, Figure 28, shows the com- 
parison in the case of a group of 112 pupils from the same 
school in high school and freshman mathematics. The fresh- 
man grading averages in this case much lower than in the 
high school, as may be seen by a glance at the chart. These 
four charts would appear then to indicate that there is closer 
correlation between the high school in question and the Col- 
lege of Letters and Science in some subjects of study than in 
others. This may be the case, although it is quite as likely 
due to arbitrary differences in the scale of marks used as has 
been indicated in the preceding chapters. 

In order to study this question satisfactorily it is necessary 
to follow the record of the individual student by some such 
method as has been suggested above in this chapter. For pur- 
poses of illustration this has been done in the case of the gen- 
eral averages of this group of pupils from the Madison high 
school. The method is the same as outlined above, and is 
shown in Charts D and E of Plate I. In this case, those who 
ranked in the first quarter of the class in high school are 
colored red, those in the second, purple, etc. (See p. 49.) The 
standings of these pupils may be easily followed by the colors 
which remain the same in the freshman distribution. If there 
were no changes between high school and university standings 
this would be indicated by an absence of change in the color 
arrangement, i. e., all the "reds" would remain in the first 
quarter of the group in the university, all the "purples" in 
the second quarter, etc. And, as a matter of fact, it may be 
seen that there is a very close correlation between the stand- 
ings of pupils in the high school and their standings in the 
university. 







^ 



^' 



/^ 



^ 



■>. 



^ 



54 



THE VXIVERSITY OF WISCOXSIN 



A final problem in this connection may be suggested, name- 
ly, as regards the character or quality of the elimination from 
school and university. There has, during the last few years 
been considerable attention given to the amount of elimina- 
tion from school. The sort of elimination is also of interest. 
In order to indicate a simple method for the study of this ques- 
tion a square has been placed about the high school grades of 
those students who did not finish the sophomore year at the 
university. While, as may readily be seen, the larger number 
who drop out for one reason or another are from the lower 
half of the class, there is a fair proportion from the upper 
half. This is a problem which has greater significance in the 
high school where the sort of elimination from school is prob- 
ably not as much related to scholastic attainment. 



VII. APPENDIX OF UNIVERSITY GRADES 

(See Chapter V.) 
TABLE I— A.<^' 

Percentages by Departments 
(Freshman and Sophomore Years) 



Ex. 

History 5.91 

English 8.4 

Mathematics 16.3 

French 19.75 

Physics 27.95 

Chemistry 21.1 

Latin 17.9 

German 19.9 

Per Cent of Total. . 14 











No. of 


G. 


F. 


P. 


X. 


Cases 


29.6 


34.9 


21.5 


8.1 


1353 


36.3 


33.8 


16.3 


5.26 


1180 


23.9 


23.1 


19.7 


17.1 


633 


36.0 


24.5 


14.3 


5.46 


567 


37.8 


21.1 


lO.S 


2.45 


204 


35 


24.6 


15.6 


3.81 


280 


46.7 


21.1 


11.2 


3.2 


313 



36.3 25.0 14.13 4.61 955 



29 



17 



5494 



(1) The following abbreviations are used,— Ex. for "Excellent," 
G. for "Good," F. for "Fair," P. for "Poor," and X. for "Condi- 
tioned" and "Failure" combined. 



SCHOOL AND UXIVERSITY GRADES 



55 



TABLE I— B. 

Percentages by Departments 

(Junior and Senior Years) 



Ex. 

1. English 18.8 

2. Political Economy. 17.2 

3. Grerman 17.4 

4. Philosophy 12.8 

5. History 13.1 

6. Education 14.6 

7. French 26. 

8. Political Science... 20.3 

9. Latin 19.3 

10. Mathematics 34.2 

11. Chemistry 21.7 

12. Physics 34.6 

13. Botany 17.5 

14. Geology 12. 



G. 


F. 


P. 


X. 


Cases 


42.3 


26.9 


9.3 


2.4 


1154 


35.9 


25. 


16.4 


5.2 


889 


49.4 


24.4 


6.5 


1.7 


796 


38.3 


27. 


15.5 


6.2 


709 


48.1 


27.9 


7.3 


3.4 


660 


53.2 


25.9 


4.7 


1.3 


443 


45.8 


20. 


5.3 


2.6 


410 


53.6 


16.8 


7.9 


1.1 


339 


57.3 


16.5 


4.7 


1.9 


314 


35.7 


15.5 


9.8 


4.6 


193 


40.7 


23.4 


10.6 


3.3 


179 


39.2 


13.8 


9.2 


3. 


130 


51.7 


19.2 


8.7 


2.6 


114 


43.1 


34.4 


5.1 


5.1 


58 



Per Cent of Total. 18.3 



44. 



24.2 



9.6 



6397 



TABLE I— C. 

Percentages by Departments 

(All Classes) 



Ex. 

History 8.3 

English 13.5 

Mathematics 20.4 

French 23.4 

Physics 30.5 

Chemistry 21.3 

Latin 18.6 

German 18.7 

Biology 12.7 

Geology 5.5 

<^> Philosophy 12.8 

"> Education 14.7 

•1' Political Science... 20.4 

<^^ Political Economy. . 17.2 



Per Cent of Total. . 15.9 











No. of 


G. 


F. 


P. 


X. 


Cases 


35.7 


32.5 


16.8 


6.5 


2022 


39.2 


30.4 


12.8 


3.8 


2334 


26.6 


21.3 


17.4 


14.1 


826 


40.1 


22.5 


10.5 


4.2 


977 


38.3 


18.2 


10.1 


2.6 


334 


37.1 


24.1 


13.6 


3.6 


468 


51.9 


18.8 


7.9 


2.5 


627 


42.4 


24.7 


10.6 


3.3 


1751 


40.1 


27.6 


14.5 


4.9 


344 


39.1 


36.2 


14.4 


4.6 


215 


38.4 


27.1 


15.5 


6.21 


709 


53.3 


25.9 


4.74 


1.35 


443 


53.6 


16.8 


7.96 


1.18 


339 


36 


25.1 


16.4 


5.3 


889 


39.5 


26.4 


13.3 


4.9 


12278 



'i> Juniors and seniors only. 



5G 



THE UNIVERSITY OF WISCONSIX 



TABLE II— A 
Percentages of Grades Assigned by Individual Instructors 



TO Freshmen and Sophomores 



Historv Ex. 

1 4.91 

2 9.84 

3 3.4 

4 7. 48 

5 1G.7 

6 9.1 

7 6.33 



G. 
26.2 
52.9 
22 
25.2 
52.4 
39.4 
27.4 



F. 

32.8 
31.6 
38.9 
37.4 
28.6 
27.3 
30.8 



P. 

26.2 

3.11 
26.7 
23.4 
2.38 
18-2 
23.6 



X. 

9.84 
2.59 
8.96 
6.54 


6.06 
11.8 



No. of 

Cases 

183 

193 

558 

107 

42 

33 

237 



1353 



English 

8 19.3 22.6 19.3 38.7 31 

9 12.5 30 37.5 12.5 7.50 40 

10 6.42 45 31.2 14.7 2.75 109 

11 1.98 33.2 45.5 12.9 6.43 202 

12 7.44 30.6 38.0 19.0 4.96 121 

13 6.31 33.7 40 14.7 5.26 95 

14 4.08 38.8 32.6 14.3 10.2 49 

15 16.7 22.8 36.0 17.55 7.01 114 

16 7.3 39.6 37.5 13.5 2.08 98 

17 16.9 50.6 19.5 11.7 1.3 77 

IS 11.4 42.9 27.2 14.3 4.29 70 

19 8.99 53.9 21.8 7.69 7.69 78 

20 6.12 25.5 23.5 37.8 7.14 98 

IISO 

Mathematics 

21 16.6 27.8 28.5 14.25 12.9 302 

22 24.1 25 15.74 19.45 15.74 108 

23 12.1 17.9 19.3 27.4 23.3 223 



633 

Prench 

24 21.2 43.8 22.5 7.5 5 80 

25 17.5 43.8 27.5 7.5 3.75 80 

26 22.3 35.7 21.4 12.5 8.03 112 

27 15.53 32 27.2 19.4 5.82 103 

28 14.5 24.2 24.2 27.4 9.67 62 

29 23.9 35.4 24.6 13.85 2.31 130 



507 



SCHOOL AND UNIVERSITY GRADES 57 



Phvsics and Chemistry 

30 27.9 37.8 

31 21.1 35 

Latin 

32 16.1 46 

33 11.77 46.2 

34 26.1 47.6 

German 

35 26.3 34.2 

36 12.03 49.1 

37 34.3 40.3 

38 11.47 34.4 

39 17.33 37.3 

40 17.9 35 

41 14.74 29.5 

42 12.32 27.4 

43 29.03 30.1 

44 21.6 42.03 

45 22.4 39.64 



21.1 


10.8 


2.45 


204 


24.6 


15.6 


3.81 


289 


20.7 


9.20 


8.04 


87 


26 


16 





119 


15.9 


7.48 


2.804 


107 


21.9 


12.3 


5.26 


114 


24.1 


11.1 


3.702 


108 


19.4 


2.984 


2.984 


67 


27.9 


22.95 


3.28 


61 


29.3 


6.66 


9.34 


75 


26 


17.1 


4.06 


123 


33.5 


18.95 


3.16 


95 


27.4 


21.95 


10.95 


73 


22.6 


14 


4.3 


93 


21.6 


12.5 


2.27 


88 


20.7 


15.53 


1.726 


58 



955 



TABLE II— B. 
Percentages of Grades Assigned to Juniors and Seniors 















No. of 


English 


Ex. 


G. 


F. 


P. 


X. 


Cases 


1 


.. 14.6 


37.8 


33.5 


11.9 


1.9 


301 


2 


. . 29.5 


50.9 


18.5 


0.9 





210 


3 


.. 22.1 


43 


25.5 


7.6 


1.7 


172 


4 


.. 13.2 


25.8 


35.7 


14.5 


10.6 


151 


5 


. . 14.7 


50 


21.3 


13.9 





122 


6 


. . 20.9 


43 


24.4 


10.4 


1.1 


86 


7 


.. 13.5 


60.8 


22.9 


2.7 





74 


Political Economy 












9 


.. 11.8 


30 


26 


22.8 


9.45 


127 


10 


. . 25.2 


46.1 


20 


7 


1.74 


115 


11 


.. 20.7 


21.6 


27.05 


18.9 


11.7 


111 


12 


.. 8.7 


45.6 


27.2 


16.5 


1.94 


103 


13 


.. 43.4 


45.8 


3.6 


7.2 





83 


14 


.. 15 


33.8 


47.7 


5 


2.5 


80 


. 15 


.. 


33.4 


26.9 


25.6 


14.1 


78 


16 


.. 31.6 


25 


29.7 


14.05 


11.8 


64 


17 


.. 6.98 


32.6 


4.7 


46.5 


9.3 


43 


18 


.. 14.6 


43.9 


26.8 


12.2 


2.44 


41 


19 


.. 


43.2 


41 


15.9 





44 



58 THE UNIVERSITY OF WISCONSIN 



German 














20 


29.9 


47.6 


17.7 


48.8 





164 


21 


8.7 


68 


22.45 





0.73 


138 


22 


9.3 


56.6 


24 


10.7 





129 


23 


24.55 


41.5 


27.35 


5.66 


.94 


106 


24 


14.6 


38.2 


30.4 


11.2 


5.63 


89 


25 


10 


50 


31.3 


7.5 


1.25 


80 


26 


17 


35.8 


32.1 


7.55 


7.55 


53 


27 


27 


37.85 


16.2 


13.5 


5.4 


37 


Philosophy 














28 


12.1 


34.6 


22.7 


23.3 


7.38 


339 


29 


8.8 


41.4 


40.4 


3.1 


6.22 


193 


30 


15.9 


36.5 


23.35 


18.7 


5.6 


107 


31 


22.9 


51.4 


17.15 


7.15 


1.43 


70 


History 














32 


14 


51.2 


31.9 


1.9 


.97 


207 


33 


5.15 


47.4 


27.75 


11.34 


8.25 


97 


34 


6.46 


40.8 


34.4 


10.75 


7.52 


93 


35 


17.15 


58.6 


22.85 


1.43 





70 


36 


15.25 


49.15 


32.2 


3.4 





59 


37 


19 


41.3 


20.7 


17.25 


1.7 


58 


Latin 














38 


17.65 


61.25 


13.72 


4.9 


2.45 


204 


39 


39 


39 


17.05 


4.88 





41 


40 


2.86 


63 


28.6 


5.71 





35 


41 


23.5 


50 


20.6 


2.94 


2.94 


34 


Mathematics 














42 


34.6 


42 


12.35 


9.88 


1.235 


81 


43 


33.9 


32.2 


20.35 


5.08 


8.48 


59 


44 


36.7 


36.7 


13.32 


10 


3.33 


30 


45 


30.4 


21.7 


17.38 


21.7 


8.7 


23 


Chemistry 














46 


31.8 


33.3 


16.7 


16.7 


1.51 


66 


47 


18.35 


32.65 


32.65 


6.12 


10.2 


49 


48 





36 


48 


16 





25 


49 


16 


68 


12 


4 





25 


Political Science 












50 


29.4 


53.6 


13 


3.9 





177 


51 


4.4 


58.2 


22 


12.1 


3.3 


91 


52 


18.3 


47.9 


19.7. 


12.7 


1.4 


71 


French 














53 


44.1 


41.5 


6.0 


5.0 


1.7 


118 


54 


26.4 


48.1 


19.8 


1.9 


3.8 


106 


55 


14.8 


43.2 


33.3 


4.9 


3.7 


81 


56 


10 


50 


31.4 


7.1 


1.4 


70 


57 


22.8 


51.4 


11.4 


11.4 


2.8 


35 



SCHOOL AND UNIVERSITY GRADES 59 

Education 

58 15.1 59.6 23.1 1.7 .35 285 

59 10.6 42.5 31.9 11.3 3.5 141 

60 11.6 50.4 36.4 1.6 85 

Physics 

61 50 35.5 6.45 8.06 62 

02 20.4 40.7 18.5 12.95 7.4 54 

Botany 

03 20 42.9 21.4 11.4 4.29 70 

64 13.64 65.9 15.9 4.55 44 

Geology 

65 12.05 43.1 34.5 5.17 5.17 58 



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